The Israelis, for instance, mount a fully credible deterrent for what must be a tiny fraction of this. Is there a cheaper way?
Fully credible against limited conventionally armed regional second or third world forces - probably.
Fully credible against one of the Big Five in a nuclear shooting match - nope and it's not even close.
To have any credibility (and therefore nuclear deterrence value) Trident has to a have a full "second strike" capability - which it does.
Another issue is the question of how visible submarines might be by 2050; it's possible in the next decade or two they may become very visible to relatively inexpensive sensors.
Assuming you mean state of the art nukes, outwith novels and movies, it will still be like looking for a carbon fibre needle in a haystack (in giant field of haystacks). It's ****ing hard to find things under the sea you know...ask the people looking for MH370 (and that's not even hiding).